ALS-XY-Wing

The ALS-XY-Wing rule is a solving technique that uses three Almost Locked Sets.

Make sure you understand the concept of Almost Locked Sets before you proceed.

How it works

Say we have three Almost Locked Sets A, B and C. Suppose

Then for any digit X that is a common candidate for A and B, we can eliminate X from any cell that sees all cells belonging to either A or B and having X as a candidate.

Observe that this technique is very similar to XY-Wing, and hence its name. The similarity can be illustrated by treating A, C and B as nodes in a chain of length three, with C being the pivot.

Note on notation

Unlike ALS-XZ and XY-Wing, which eliminates the digit Z, the ALS-XY-Wing eliminates the digit X instead. Unfortunately, this inconsistent notation is widely used by the Sudoku community.

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